To be most efficient antennas need to resonate at the desired frequency.
In order to do that, the length needs to bear some relationship with the wavelength.
We normally think that when a voltage is applied to a wire, the whole wire is at that voltage immediately, but when the length of the wire approaches the wavelength, odd stuff starts to happen (or more precisely the odd stuff that happens starts to have an effect that matters)
Imagine that I suddenly apply a voltage to the end of a wire. The wire does not magically take that potential suddenly, but a wavefront travels down the wire at the speed of light.
Another aside, it's the speed of light in that medium, not the speed of light in a vacuum. You might think that it's the speed of light in copper, but it's actually the speed of light in the conductor (and for this purpose "the conductor" also includes distributed capacitances and inductances -- so spacing and insulating materials are significant). Coax cable has a specified velocity factor that tells you the relative speed of light in that as opposed to a vacuum. The same is true of tracks on a PCB (in that it in slower, not that it is specified) -- ground plane, distances to other conductors, and bends all contribute to the speed of the signal.
Anyway, we have a wavefront traveling up there wire at the speed of light in that conductor. When it reaches the end (or a discontinuity), the wavefront can be reflected. That reflected wavefront is reflected in direction and magnitude.
Let's, for the sake of the example, assume that the wavefront was +1V. As it reflects, a +1V wavefront starts coming back.
If we had an oscilloscope we would see the voltage on one end on the cable jump up to 1V, then after the reflection returns, step up to 2V. (See here). <-- that video also tells you more about what a discontinuity is.
A step function isn't a "frequency", so we need to think about what happens when the signal is a sine wave. You can think of the sine wave as progressing along the wire, then getting reflected back. If the conductor is exactly a 1/4 wavelength, then the reflection is exactly 180 degrees out of phase. This will cause the voltage at the beginning of the cable to always be zero! Furthermore, the voltage will vary along the cable. This standing wave is what causes the conductor to radiate energy.
At the frequency increases the effect diminishes, and then increases as you get to the next relationship between frequency and length.
Interestingly enough, this standing wave affects both current and voltage. So, in direct violation of rules you think you know, the voltage and the current vary along a single conductor.
That's a simple (hopefully not too simple) explanation.
P.s. the thing about speed of light means that the length is somewhat less than the calculated using the speed of light in a vacuum. (See here -- it can be less than 50%)
In order to do that, the length needs to bear some relationship with the wavelength.
We normally think that when a voltage is applied to a wire, the whole wire is at that voltage immediately, but when the length of the wire approaches the wavelength, odd stuff starts to happen (or more precisely the odd stuff that happens starts to have an effect that matters)
Imagine that I suddenly apply a voltage to the end of a wire. The wire does not magically take that potential suddenly, but a wavefront travels down the wire at the speed of light.
Another aside, it's the speed of light in that medium, not the speed of light in a vacuum. You might think that it's the speed of light in copper, but it's actually the speed of light in the conductor (and for this purpose "the conductor" also includes distributed capacitances and inductances -- so spacing and insulating materials are significant). Coax cable has a specified velocity factor that tells you the relative speed of light in that as opposed to a vacuum. The same is true of tracks on a PCB (in that it in slower, not that it is specified) -- ground plane, distances to other conductors, and bends all contribute to the speed of the signal.
Anyway, we have a wavefront traveling up there wire at the speed of light in that conductor. When it reaches the end (or a discontinuity), the wavefront can be reflected. That reflected wavefront is reflected in direction and magnitude.
Let's, for the sake of the example, assume that the wavefront was +1V. As it reflects, a +1V wavefront starts coming back.
If we had an oscilloscope we would see the voltage on one end on the cable jump up to 1V, then after the reflection returns, step up to 2V. (See here). <-- that video also tells you more about what a discontinuity is.
A step function isn't a "frequency", so we need to think about what happens when the signal is a sine wave. You can think of the sine wave as progressing along the wire, then getting reflected back. If the conductor is exactly a 1/4 wavelength, then the reflection is exactly 180 degrees out of phase. This will cause the voltage at the beginning of the cable to always be zero! Furthermore, the voltage will vary along the cable. This standing wave is what causes the conductor to radiate energy.
At the frequency increases the effect diminishes, and then increases as you get to the next relationship between frequency and length.
Interestingly enough, this standing wave affects both current and voltage. So, in direct violation of rules you think you know, the voltage and the current vary along a single conductor.
That's a simple (hopefully not too simple) explanation.
P.s. the thing about speed of light means that the length is somewhat less than the calculated using the speed of light in a vacuum. (See here -- it can be less than 50%)
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